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Cell Lab a MATLAB environment for the development of 2D cell method codes

Dipartimento Ingegneria Elettrica Politecnico di Torino (ITALY). Cell Lab a MATLAB environment for the development of 2D cell method codes. Applications of the Cell Method in Engineering. Outline. Introduction Why MATLAB Philosophy Features Ongoing work Examples electrostatic field

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Cell Lab a MATLAB environment for the development of 2D cell method codes

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  1. Dipartimento Ingegneria Elettrica Politecnico di Torino (ITALY) Cell Lab a MATLAB environment for thedevelopment of 2D cell method codes Applications of the Cell Method in Engineering

  2. Outline • Introduction • Why MATLAB • Philosophy • Features • Ongoing work • Examples • electrostatic field • magnetostatic field

  3. Introduction • Dual lab is not • an all-in-one program to solve field problems • a program to solve a particular field problem (e.g. electrostatic solver) • an established code • ... but rather it is • a collection of MATLAB routines useful to build your own solver • an environment for testing and fast-prototyping new formulations • a didactical instrument for the Cell Method

  4. Why MATLAB • Why MATLAB? • It is easy to use • Many built-in functions • Powerful postprocessing capabilities • but, above all • MATLAB has very efficient routines to handle sparse matrices

  5. Philosophy • MATLAB-like implementation • Use exactly the primal (dual) cycle • Solving system can be built by using (sparse) matrix operations • e.g. for electrostatic problems known unknown primal cycle

  6. Philosophy • open source, downlodable and editable • does not require any extra MATLAB toolbox (e.g. PDE) • encourage the exchanges among researchers

  7. Features • 2D mesh import • quadrangle • diagonal constitutive matrix • triangle • requires the definition of shape functions • nondiagonal sparse constitutive matrix

  8. Features • Preprocessor • data structure with primal mesh information • data structure with dual mesh information • build incidence matrices (0, +1, -1) • boundary conditions • Solver: MATLAB built-in functions • factorization (lu, chol, qr, luinc) • direct methods (\ operator) • iterative methods (bicg, bicgstab, cgs, gmres, lsqr, minres, pcg, qmr, symmlq) • Postprocessor • standard MATLAB tool • customized routines

  9. Ongoing work • implementation of a quadrangular mesh generator • import of MATLAB based simplex mesh generator DISTMESH (www-math.mit.edu/~persson/mesh/) • extension to 3D problems (hexaedra and tetraedra) • thorough phase of testing new formulations in different application fields

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